Large deviations for nonuniformly hyperbolic systems
Large deviations for nonuniformly hyperbolic systems
复制标题
DOI：
10.1090/s0002-9947-08-04520-0
复制
发表时间：
2008-01-01
影响因子：
1.3
通讯作者：
Nicol, Matthew
中科院分区：
文献类型：
--
作者：
Melbourne, Ian;Nicol, Matthew
我们得到了一大类非一致双曲型系统的大偏差估计：即由相关系数可求和衰减的Young塔所模拟的系统。在相关性指数衰减的情况下，我们得到了由速率函数给出的指数大偏差估计。在多项式相关衰减的情况下，我们得到了多项式大偏差估计，并给出了这些估计本质上是最优的例子。与许多大偏差的处理不同，我们的方法不依赖于热力学形式。因此，对于Holder可观测，在平衡测度空间未知为单点的情况下，我们可以得到指数估计，在没有唯一平衡测度的情况下，我们可以得到多项式估计。
We obtain large deviation estimates for a large class of nonuniformly hyperbolic systems: namely those modelled by Young towers with summable decay of correlations. In the case of exponential decay of correlations, we obtain exponential large deviation estimates given by a rate function. In the case of polynomial decay of correlations, we obtain polynomial large deviation estimates, and exhibit examples where these estimates are essentially optimal.In contrast with many treatments of large deviations, our methods do not rely on thermodynamic formalism. Hence, for Holder observables we are able to obtain exponential estimates in situations where the space of equilibrium measures is not known to be a singleton, as well as polynomial estimates in situations where there is not a unique equilibrium measure.